If the radius of a circle is doubled, what effect does this have on the area of the circle? On the circumference? Explain why your result makes sense.
What you have to remember here is the formulas for area and circumference of a circle.
The area of a circle is equal to the square of its radius times pi. The circumference of a circle is equal to the diameter times pi.
So, let's look at what happens if you double the radius of a circle -- say from 2 to 4.
The area will go from 12.56 to 50.24. This means that it has quadrupled. The reason for this is that you square the radius. So when you double the radius, the area goes up by 4 times because 2 squared is 4. The area will always go up by the square of how much the radius goes up.
By contrast, the circumference will only double -- from 12.56 to 25.12 because you do not square the radius (or diameter) -- you just multiply it by pi. So the circumference will go up by the same percent that the radius does.
Area of a circle is directly proportional to the square of radius of the circle while the circumference is proportional to the radius of the circle. This means that if the radius of a circle is increased x times, then its area will be increased to x^2 times the original area, and the circumference will increase to x times the original circumference.
Thus when the radius is doubled, or in other words if radius mad 2 time the original radius, the area of circle will become 2^2 = 4 time the original area. The circumference will become 2 times the original circumference.
We can calculate exact area and circumference of a circle from its radius using the following equations:
Area of circle = (pi/4)*r^2
Circumference of circle = 2*pi*r
Where r is the radius of the circle.
The area of circle for double radius is 4 times the area of single radius.
For radius 1 the area is pi*1^2=pi sq unit.and for 2 the area is pi*2^2 = 4pi sq units.
For radius 3 , area = pi*3^2 = 9pi sq units and doubling the radius 3 we get a radius 6 and the area of circle for 6 units is pi*6^2 = pi*36 = 36pi sq units which 4 times 9pi .
In general area of circle of radius r is pi*^2 and area of circle of radius 2r is pi*(2r)^2 = p*2r*2r = 4pir^2.